Web sites of companies offering products or services show a link or button asking you to request them to call you back.
It's usually presented in a very prominent way, for example a red button labeled "Request a call back!" that stays fixed on an edge of the pages.
If I see such a button, I'm wondering why should I wait for them to call? If I want to talk, I'll call myself.
If they want to talk to me, I would expect they would at least show me the number to call with that button as alternative. That's not allways the case - which indicated that it's not the main point that they want to talk to me.
The button would make sense if it would be shown only as an alternative to the phone number at times of the day when I can not call them myself. I did not check, but assume that's not the case. (If it is, it's confusing at least, as indicated by this question.)
I do understand the aspect of the button to grab my attention by commanding me to do something. I'm not asking about all that would allso apply to a "Call us at 000-000000!" buton.
The call to action makes sense; Trying to talk to me personally makes lots of sense, at least with a complex and low volume product or product range.
But why should I want to wait for them? It's not even obvious how long! And if I'm curious enough now, that does not mean I'm still later.
As an example, http://trotec-leipzig.de, which offers laser cutting machines, has a button "We call you back." (German: "Wir rufen sie zurueck.") at the right edge of each page.
Pressing the button shows a form requesting some details (curiously most are mandatory).
The screenshot shows that form iin German language;
The labels translate to "Callback form", "Get in contact with us:", "Name", "Phone", "email", "At which time would you like to be called?" (to choose a day of the week, and a time range of the day), "Subject", and "Zip code/City".
At the same time, it shows the button, just as ono any other page.
The form was reached by pressing a button like this on a dfferent page. On this page, it does not actually make sense - except to show you how it looks without a separate screenshot.